2
$\begingroup$

enter image description here

How do you find the phase and inverse Fourier transform of this frequency spectrum?

$\endgroup$
  • 3
    $\begingroup$ Is this a homework assignment? $\endgroup$ – hotpaw2 Jun 23 '14 at 19:15
  • $\begingroup$ no it isn't.... $\endgroup$ – martinap Jun 23 '14 at 19:18
  • $\begingroup$ The spectrum is usually complex. Sometimes the definition implies "magnitude", which is real, but in that case it would be positive. Perhaps you could clear this up a little from the context of the book? In this meant to be a Fourier representation of a signal which happens to be purely real? $\endgroup$ – Phonon Jun 23 '14 at 22:45
1
$\begingroup$
  1. The magnitude is given by $ {\left| X \left( f \right) \right|} $ hence it is 6.
  2. Assuming all data is given in the graph, the function isn't complex it is only negative -> Phase is -180 degrees.
  3. You should use its symmetry. Without over thinking it, It could be generated by a window on the center convolved with 2 deltas (Shifted) -> Sinc in time multiplied by 2 exponentials.
$\endgroup$
  • 1
    $\begingroup$ The magnitude is $|X(f)|$, not $|X(f)|^2$ (which is the squared magnitude). So its value is 6, not 36. $\endgroup$ – Matt L. Jun 24 '14 at 7:43
  • $\begingroup$ By the book you're correct. Yet usually this term is abused, and I assumed this to be the case :-) (Since otherwise it would be seem trivial). Anyhow, fixed it. $\endgroup$ – Royi Jun 24 '14 at 7:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.